ANKARA, Jan 30 (Reuters) - Turkish Prime Minister Tayyip Erdogan's feud with U.S.-based Muslim cleric Fethullah Gulen has damaged the reputation of both, but Erdogan's party would still win an election if one were called this weekend, a survey showed on Thursday.

A corruption scandal led to the resignation of three government ministers last month, as well as the detention of businessmen close to Erdogan, who has portrayed the investigation as a "judicial coup" attempt by Gulen supporters.

Gulen's Hizmet ("Service") movement is widely believed to have considerable influence in the police and judiciary and the government has transferred thousands of police officers and more than a hundred prosecutors in response to the inquiry.

"Both sides are losing prestige rapidly," Ozer Sancar, the head of the MetroPoll polling company said. "The approval rates for President (Abdullah) Gul as well as Prime Minister Erdogan are at their lowest in years."

Erdogan's approval rating tumbled to 39.4 percent this month from 48.1 percent in December and 59.1 percent a year earlier, according to the survey.

Gul's rating fell to 46.5 percent in January from 63.3 percent in December and 76.0 percent 12 months earlier.

But if a parliamentary election were held on Sunday, Erdogan's AK Party would still garner the highest number of votes, albeit far fewer than the 50 percent it obtained in the 2011 election, the survey should.

The AKP would attract 43.2 percent of votes if an election took place on Sunday, including distributed votes of those undecided. The main opposition Republican People's Party (CHP) would secure 28.1 percent, up from 26 percent in the 2011 election.

There was majority negative sentiment towards Gulen and his movement, whose supporters claim to number millions worldwide.

Some 60 percent of those polled describe their overall view of Gulen's movement as negative and 57 percent believe it to have established what Erdogan has described as a "parallel state" within the state bureaucracy.

Conducted between Jan. 14 and Jan. 21 among 1,545 people, the results of the MetroPoll research show the public was mostly sceptical of Erdogan's portrayal of the corruption inquiry as a "judicial coup".

About 42 percent of those polled believed the probe, which became public on Dec. 17, was a genuine graft inquiry, while 24 percent believed it was a coup attempt against the government.

Around 60 percent of the respondents believed the government had tried to cover up the corruption allegations and had exerted pressure on the police and judiciary. (Reporting by Humeyra Pamuk; Editing by Daren Butler and Alistair Lyon)